Circles Can be Cool Too!

Geometry Level 4

Circle \(\omega _ {1}\) with center \(A\) and circle \(\omega _{2}\) with center \(B\) have radii \(7\) and \(2\) respectively. The two circles intersect at points \(T\) and \(Y\) such that \(TY = 2\). Let \(P\) be a point outside of both circles such that \(PA = 9 \) and \(PB = 6\). The area of \(\bigtriangleup PAB\) can be expressed as \(\frac{a\sqrt{b}}{c}\) such that \(b\) is a square-free integer and \(a\) and \(c\) are relatively prime integers. Find \(a+b+c\).

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